Use of geometric prior information in Bayesian tomographic image reconstruction: A preliminary report

摘要

In this paper we examine the possibility of using pure geometrical information from a prior image to assist in the reconstruction of tomographic data sets with lower number of counts. The situation can arise in dynamic studies, for example, in which the sum image from a number of time frames is available, defining desired regions-of-interest (ROI's) with good accuracy, and the time evolution of uptake in those ROI's needs to be obtained from the low count individual data sets. 'the prior information must be purely geometrical in such a case, so that the activity in the ROI's of the prior does not influence the estimated uptake from the individual time frames. It is also desired that the prior does not impose any other conditions on the reconstructions, i.e., no smoothness or deviation from a known set of values is desired. We attack this problem in the framework of Vision Response Functions (VRFs), based on the work done by J.J. Koenderink in Utrecht. We show that there are assemblies of VRF's that can be presented in a form that is invariant with respect to rotations and translations and that some functions of those invariants can convey the desired geometric prior information independent of the level of activity in the ROI'S, except at very low levels.